The dependence between survival times and covariates is described e.g. by proportional hazard models. We consider partly parametric Cox models and discuss here the estimation of interesting parameters. We represent the ma- ximum likelihood approach and extend the results of Huang (1999) from linear to nonlinear parameters. Then we investigate the least squares esti- mation and formulate conditions for the a.s. boundedness and consistency of these estimators.

Vid analys av vattenprover tagna från t.ex. ett vattendrag betäms halten av olika ämnen. Dessa halter är ofta beroende av vattenföringen. Det är av intresse att ta reda på om observerade förändringar i halterna beror på naturliga variationer eller är orsakade av andra faktorer. För att undersöka detta har föreslagits en statistisk tidsseriemodell som innehåller okända parametrar. Modellen anpassas till uppmätta data vilket leder till ett underbestämt ekvationssystem. I avhandlingen studeras bl.a. olika sätt att säkerställa en unik och rimlig lösning. Grundidén är att införa vissa tilläggsvillkor på de sökta parametrarna. I den studerade modellen kan man t.ex. kräva att vissa parametrar inte varierar kraftigt med tiden men tillåter årstidsvariationer. Det görs genom att dessa parametrar i modellen regulariseras. Detta ger upphov till ett minsta kvadratproblem med en eller två regulariseringsparametrar. I och med att inte alla ingående parametrar regulariseras får vi dessutom ett partiellt regulariserat minsta kvadratproblem. I allmänhet känner man inte värden på regulariseringsparametrarna utan problemet kan behöva lösas med flera olika värden på dessa för att få en rimlig lösning. I avhandlingen studeras hur detta problem kan lösas numeriskt med i huvudsak två olika metoder, en iterativ och en direkt metod. Dessutom studeras några sätt att bestämma lämpliga värden på regulariseringsparametrarna. I en iterativ lösningsmetod förbättras stegvis en given begynnelseapproximation tills ett lämpligt valt stoppkriterium blir uppfyllt. Vi använder här konjugerade gradientmetoden med speciellt konstruerade prekonditionerare. Antalet iterationer som krävs för att lösa problemet utan prekonditionering och med prekonditionering jämförs både teoretiskt och praktiskt. Metoden undersöks här endast med samma värde på de två regulariseringsparametrarna. I den direkta metoden används QR-faktorisering för att lösa minsta kvadratproblemet. Idén är att först utföra de beräkningar som kan göras oberoende av regulariseringsparametrarna samtidigt som hänsyn tas till problemets speciella struktur. För att bestämma värden på regulariseringsparametrarna generaliseras Reinsch’s etod till fallet med två parametrar. Även generaliserad korsvalidering och en mindre beräkningstung Monte Carlo-metod undersöks. / Statistical analysis of data from rivers deals with time series which are dependent, e.g., on climatic and seasonal factors. For example, it is a well-known fact that the load of substances in rivers can be strongly dependent on the runoff. It is of interest to find out whether observed changes in riverine loads are due only to natural variation or caused by other factors. Semi-parametric models have been proposed for estimation of time-varying linear relationships between runoff and riverine loads of substances. The aim of this work is to study some numerical methods for solving the linear least squares problem which arises. The model gives a linear system of the form A1x1 + A2x2 + n = b1. The vector n consists of identically distributed random variables all with mean zero. The unknowns, x, are split into two groups, x1 and x2. In this model, usually there are more unknowns than observations and the resulting linear system is most often consistent having an infinite number of solutions. Hence some constraint on the parameter vector x is needed. One possibility is to avoid rapid variation in, e.g., the parameters x2. This can be accomplished by regularizing using a matrix A3, which is a discretization of some norm. The problem is formulated as a partially regularized least squares problem with one or two regularization parameters. The parameter x2 has here a two-dimensional structure. By using two different regularization parameters it is possible to regularize separately in each dimension. We first study (for the case of one parameter only) the conjugate gradient method for solution of the problem. To improve rate of convergence blockpreconditioners of Schur complement type are suggested, analyzed and tested. Also a direct solution method based on QR decomposition is studied. The idea is to first perform operations independent of the values of the regularization parameters. Here we utilize the special block-structure of the problem. We further discuss the choice of regularization parameters and generalize in particular Reinsch’s method to the case with two parameters. Finally the cross-validation technique is treated. Here also a Monte Carlo method is used by which an approximation to the generalized cross-validation function can be computed efficiently.

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In regression with near collinear explanatory variables, the least squares predictor has large variance. Ordinary least squares regression (OLSR) often leads to unrealistic regression coefficients. Several regularized regression methods have been proposed as alternatives. Well-known are principal components regression (PCR), ridge regression (RR) and continuum regression (CR). The latter two involve a continuous metaparameter, offering additional flexibility. For a univariate response variable, CR incorporates OLSR, PLSR, and PCR as special cases, for special values of the metaparameter. CR is also closely related to RR. However, CR can in fact yield regressors that vary discontinuously with the metaparameter. Thus, the relation between CR and RR is not always one-to-one. We develop a new class of regression methods, LSRR, essentially the same as CR, but without discontinuities, and prove that any optimization principle will yield a regressor proportional to a RR, provided only that the principle implies maximizing some function of the regressor's sample correlation coefficient and its sample variance. For a multivariate response vector we demonstrate that a number of well-established regression methods are related, in that they are special cases of basically one general procedure. We try a more general method based on this procedure, with two meta-parameters. In a simulation study we compare this method to ridge regression, multivariate PLSR and repeated univariate PLSR. For most types of data studied, all methods do approximately equally well. There are cases where RR and LSRR yield larger errors than the other methods, and we conclude that one-factor methods are not adequate for situations where more than one latent variable are needed to describe the data. Among those based on latent variables, none of the methods tried is superior to the others in any obvious way.

In indoor environment, the multi-sensor system can be used as an efficient solution for target location process, in terms of lower estimation cost, due to the factor that sensors have the advantages of low power, simple, cheap, and low operation complexity. However, the location methods and the placements of designed multisensor have great impact on the location performance. Based on the time difference of arrival (TDOA), the present research utilizes linear-correction spherical-interpolation (LCSI) method to estimate the location of its targets. The method is a combination of the linear-correction least-squares method and the spherical-interpolation method. Apart from the usual process of iterative, nonlinear minimization, and consequently, under the influence of noise interference and target-sensor geometry, the spherical-interpolation method will produce better results; therefore, SI method is used in place of the LS part of the LCLS method and named as the LCSI method. The objective is to correct the SI method to generate a better estimate performance. In addition to the performance issues, the limitation of the methods will also be examined. The geometric dilution of precision (GDOP) of the TDOA location method in the 3-D scenario is demonstrated with the effects on location performance of both inside and outside of the multi-sensor formation. Programmed 3-D scenario are used in the simulations, where cases with three different multiple sensor formations and two different target heights are investigated. From the simulation results of various location methods, it can be seen that LCSI has has its advantages over other methods in the wireless TDOA location.

Support for the use of progress monitoring results for high-stakes decisions is emerging in the literature, but few studies support the reliability of the measures for this level of decision-making. What little research exists is limited to oral reading fluency measures, and their reliability for progress monitoring (PM) is not supported. This dissertation explored methods rarely applied in the literature for summarizing and analyzing progress monitoring results for medium- to high-stakes decisions. The study was conducted using extant data from 92 "low performing" third graders who were progress monitored using mathematics concept and application measures. The results for the participants in this study identified 1) the number of weeks needed to reliably assess growth on the measure; 2) if slopes differed when results were analyzed with parametric or nonparametric analyses; 3) the reliability of growth; and 4) the extent to which the group did or did not meet parametric assumptions inherent in the ordinary least square regression model. The results indicate reliable growth from static scores can be obtained in as few as 10 weeks of progress monitoring. It was also found that within this dataset, growth through parametric and nonparametric analyses was similar. These findings are limited to the dataset analyzed in this study but provide promising methods not widely known among practitioners and rarely applied in the PM literature.

We consider the application of high-order spectral/hp finite element technology to the numerical solution of boundary-value problems arising in the fields of fluid and solid mechanics. For many problems in these areas, high-order finite element procedures offer many theoretical and practical computational advantages over the low-order finite element technologies that have come to dominate much of the academic research and commercial software of the last several decades. Most notably, we may avoid various forms of locking which, without suitable stabilization, often plague low-order least-squares finite element models of incompressible viscous fluids as well as weak-form Galerkin finite element models of elastic and inelastic structures. The research documented in this dissertation includes applications of spectral/hp finite element technology to an analysis of the roles played by the linearization and minimization operators in least-squares finite element models of nonlinear boundary value problems, a novel least-squares finite element model of the incompressible Navier-Stokes equations with improved local mass conservation, weak-form Galerkin finite element models of viscoelastic beams and a high-order seven parameter continuum shell element for the numerical simulation of the fully geometrically nonlinear mechanical response of isotropic, laminated composite and functionally graded elastic shell structures. In addition, we also present a simple and efficient sparse global finite element coefficient matrix assembly operator that may be readily parallelized for use on shared memory systems. We demonstrate, through the numerical simulation of carefully chosen benchmark problems, that the finite element formulations proposed in this study are efficient, reliable and insensitive to all forms of numerical locking and element geometric distortions.

Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts. Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems. Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy. Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.

Jag använder ett från Världsbanken nyligen utkommet datamaterial över institutionell kvalitet i världens länder för att i en replikeringsstudie undersöka sambandet mellan institutionell utveckling och ekonomisk tillväxt. Modellen har med framgång redan tidigare använts, men i detta arbete är tidsperioden en senare och datamaterialet enligt min bedömning av högre kvalitet. För att kunna göra det senare uttalandet och analysera resultaten på ett uttömmande sätt, innefattar arbetet en översiktlig presentation av institutionella teorier. Eftersom undersökt samband i utgångsläget antas uppvisa dubbelriktad kausalitet, använder jag ett ekonometriskt tillvägagångssätt innehållande instrumentering för att trygga validiteten. Sammantaget visar resultaten en enkelriktad, positiv kausaleffekt från institutionell kvalitet till ekonomisk tillväxt. Det är en bit kvar till en verkligt fruktbar modellkonstruktion, samtidigt som arbetet pekar på att institutioner hör hemma i en sådan.

Let P be an n×n partial Latin square every non-empty cell of which lies in a fixed row r, a fixed column c or contains a fixed symbol s. Assume further that s is the symbol of cell (r,c) in P. We prove that P is completable to a Latin square if n≥8 and n is divisible by 4, or n≤7 and n∉{3,4,5}. Moreover, we present a polynomial algorithm for the completion of such a partial Latin square.